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Directed Polymers in Random Environments

2017-01-26 Mathematics
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Release : 2017-01-26
Genre : Mathematics
Kind : eBook
Book Rating : 878/5 ( reviews)

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Book Synopsis Directed Polymers in Random Environments by : Francis Comets

Download or read book Directed Polymers in Random Environments written by Francis Comets. This book was released on 2017-01-26. Available in PDF, EPUB and Kindle. Book excerpt: Analyzing the phase transition from diffusive to localized behavior in a model of directed polymers in a random environment, this volume places particular emphasis on the localization phenomenon. The main questionis: What does the path of a random walk look like if rewards and penalties are spatially randomly distributed?This model, which provides a simplified version of stretched elastic chains pinned by random impurities, has attracted much research activity, but it (and its relatives) still holds many secrets, especially in high dimensions. It has non-gaussian scaling limits and it belongs to the so-called KPZ universality class when the space is one-dimensional. Adopting a Gibbsian approach, using general and powerful tools from probability theory, the discrete model is studied in full generality. Presenting the state-of-the art from different perspectives, and written in the form of a first course on the subject, this monograph is aimed at researchers in probability or statistical physics, but is also accessible to masters and Ph.D. students.

The Directed Polymer in a Random Environment

1996
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Release : 1996
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Book Synopsis The Directed Polymer in a Random Environment by : John M. Noble

Download or read book The Directed Polymer in a Random Environment written by John M. Noble. This book was released on 1996. Available in PDF, EPUB and Kindle. Book excerpt:

Random Polymers

2009-04-09 Mathematics
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Release : 2009-04-09
Genre : Mathematics
Kind : eBook
Book Rating : 338/5 ( reviews)

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Book Synopsis Random Polymers by : Frank den Hollander

Download or read book Random Polymers written by Frank den Hollander. This book was released on 2009-04-09. Available in PDF, EPUB and Kindle. Book excerpt: Polymer chains that interact with themselves and/or with their environment are fascinating objects, displaying a range of interesting physical and chemical phenomena. The focus in this monograph is on the mathematical description of some of these phenomena, with particular emphasis on phase transitions as a function of interaction parameters, associated critical behavior and space-time scaling. Topics include: self-repellent polymers, self-attracting polymers, polymers interacting with interfaces, charged polymers, copolymers near linear or random selective interfaces, polymers interacting with random substrate and directed polymers in random environment. Different techniques are exposed, including the method of local times, large deviations, the lace expansion, generating functions, the method of excursions, ergodic theory, partial annealing estimates, coarse-graining techniques and martingales. Thus, this monograph offers a mathematical panorama of polymer chains, which even today holds plenty of challenges.

A Condition for Weak Disorder for Directed Polymers in Random Environment

2003
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Release : 2003
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Book Synopsis A Condition for Weak Disorder for Directed Polymers in Random Environment by : Matthias Birkner

Download or read book A Condition for Weak Disorder for Directed Polymers in Random Environment written by Matthias Birkner. This book was released on 2003. Available in PDF, EPUB and Kindle. Book excerpt:

Directed Polymers in Random Media

2016
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Release : 2016
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Book Synopsis Directed Polymers in Random Media by : Vu-Lan Nguyen

Download or read book Directed Polymers in Random Media written by Vu-Lan Nguyen. This book was released on 2016. Available in PDF, EPUB and Kindle. Book excerpt: The thesis focuses on (mostly 1 + 1 dimensional) directed polymers in random media. These are classical and celebrated models in the statistical mechanics of disordered systems and describe a one dimensional interface interacting with a d + 1-dimensional random environment where it is immersed. A very important question is to understand, in the limit where the polymer's length tends to infinity and for a typical realization of the environment, the geometric properties of the polymer: typical transversal displacement of the endpoint and its fluctuations, polymer localization at strong disorder around typical tubes determined by disorder... A strictly related problem of great interest is to study the fluctuations of the free energy. The main focus is on the so-called log-gamma polymer. This model, introduced by Seppalainen, is obtained by making a specific choice for the disorder law: the random variables are inverse Gamma variables. For this specific disorder choice, he proved that the variance of the log of the partition function is of order N"2/3, as expected by KPZ theory. This was refined into a full limit theorem Tracy -Widom type fluctuations) by Corwin, O'Connell, Seppalainen and Zygouras, via an explicit formula for the Laplace transform of a single partition function. It was until now an open problem to compute correlations between partition functions with different end-points and to study the asymptotic distribution of the polymer's endpoint. The present thesis addresses, among others, these two very challenging problems. On the other hand, we consider applications of stochastic orders on the study of directed polymer and disordered systems.

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